Answer:
[tex]a_{n}=\frac{a_{n-1}}{2}[/tex]
Step-by-step explanation:
Let's look a the sequence:
[tex]3, \frac{3}{2} ,\frac{3}{4} ,\frac{3}{8}[/tex]
we can see that
[tex]\frac{3}{2}=3*\frac{1}{2}[/tex]
and
[tex]\frac{3}{4} =\frac{3}{2}*\frac{1}{2}[/tex]
and
[tex]\frac{3}{8}=\frac{3}{4} *\frac{1}{2}[/tex]
so each next number is equal to the previous number multiplied by [tex]\frac{1}{2}[/tex] or, in other other words, is the previous number divided by 2.
So the recursive formula must be:
[tex]a_{n}=\frac{a_{n-1}}{2}[/tex]
where [tex]a_{n}[/tex] is a number in the sequence, and [tex]a_{n-1}[/tex] is the immediate previous number.
